Outline

1 / 51

# Outline - PowerPoint PPT Presentation

Outline. Gear Theory Fundamental Law of Gearing Involute profile Nomenclature Gear Trains Loading Stresses. the angular velocity ratio of the gears of a gearset must remain constant throughout the mesh. gear. pinion. pitch circle, pitch diameter d, pitch point.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Outline' - JasminFlorian

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Outline
• Gear Theory
• Fundamental Law of Gearing
• Involute profile
• Nomenclature
• Gear Trains
• Stresses

the angular velocity ratio of the gears of a gearset must remain constant throughout the mesh

gear

pinion

pitch circle, pitch diameter d, pitch point

Fundamental Law of Gearing

functionally, a gearset is a device to exchange torque for velocity

P=T

What gear tooth shape can do this?

Towards the Involute Profile

A belt connecting the two cylinders

line of action, pressure angle 

Profile of the Involute Profile

pressure angle, line of action, length of action, addendum

Involute in Action

video from http://www.howstuffworks.com

Nomenclature

Figure 11-8

Pitches, Etc.

circular pitch (mm, in.)

base pitch (mm, in.)

diametral pitch (teeth/in.)

module (mm/teeth)

Velocity Ratio

pitches must be equal for mating gears, therefore

Contact Ratio

average number of teeth in contact at any one time

=

length of action divided by the base pitch, or,

where C=center distance=(Ng+Np)*1/pd*1/2

Minimum # of Teeth

minimum # of teeth to avoid undercutting with gear and rack

Outline
• Gear Theory
• Fundamental Law of Gearing
• Involute profile
• Nomenclature
• Gear Trains
• Stresses
Simple Gear Train
• Fine for transmitting torque between
• shafts in close proximity
• when mv does not need to be too large
• Use third gear (“idler”) only for directional reasons (not for gear reduction)
Outline
• Gear Theory
• Fundamental Law of Gearing
• Involute profile
• Nomenclature
• Gear Trains
• Stresses

Because Tp is constant, should Wt be static for a tooth?

(see board for figure or page 711 in book)

• Given:
• pinion is driving gear with 50hp at 1500 rpm
• Np=20
• mv=2 (a.k.a., mg=2)
• pd=4 /in.
• =20 degrees
• Find:
Outline
• Gear Theory
• Fundamental Law of Gearing
• Involute profile
• Nomenclature
• Gear Trains
• Stresses

Lewis, 1892, first formulation of gear tooth fatigue failure

Gear Failure

Surface Failure

• from bending of teeth
• infinite life possible
• failure can be sudden
• from contact b/n of teeth
• infinite life not possible

J Kv Km Ka Ks KB KI

AGMA Gear Stress Formula

many assumptions: see page 714…

…including that the contact ratio 1<mp<2

JKv Km Ka Ks KB KI

Bending Strength Geometry Factor
• from tables on pgs. 716-718
• Inputs
• pinion or gear
• number of teeth
• pressure angle

Jp=0.34, Jg=0.38

Finding J for the Example
• pinion is driving gear with 50hp at 1500 rpm
• Np=20, Ng=40
• pd=4 /in.
• =20 degrees
• Wt=420 lb.

JKv Km Ka Ks KB KI

Dynamic (Velocity) Factor

to account for tooth-tooth impacts and resulting vibration loads

from Figure 11-22 or from Equations 11.16-11.18 (pages 718-719)

• Inputs needed:
• Quality Index (Table 11-7)
• Pitch-line Velocity
Determining Kv for the Example

(well below Vt,max)

therefore, Qv=10

JKvKm Ka Ks KB KI

to account for distribution of load across face

8/pd < F < 16/pd

can use 12/pd as a starting point

Km for the Example

F=12/pd=3 in.

Km=1.63

JKv KmKaKs KB KI

Application Factor, Ka

to account for non-uniform transmitted loads

for example, assume that all is uniform

JKv Km Ka Ks KB KI

Other Factors

Ks

to account for size

Ks=1 unless teeth are very large

KB

to account for gear with a rim and spokes

KB=1 for solid gears

KI

KI=1 for non-idlers, KI=1.42 for idler gears

similar concept to Se, but particularized to gears

Table 11-20

Figure 11-25 for steels

Sfb´

Sfb´ 

Hardness

Compared to What??

b is great, but what do I compare it to?

Life Factor KL

to adjust test data from 1E7 to any number of cycles

Temperature & Reliability Factors

KT=1 if T < 250°F

see Equation 11.24a if T > 250°F

Sfb´= 13ksi

Table 11-20

N=(450 rev/min)(60 min/hr)(8 hr/dy)(250 dy/yr)(10 yrs)=5.4E8 revs

KL=1.3558N–0.0178=0.948

Fatigue Bending Strength for Example

Class 40 Cast Iron

450 rpm, 8 hours/day, 10 years

T = 80°F

Reliability=99%

Sfb = (0.948)13ksi = 12.3 ksi

Safety Factor

Nbpinion =(12300 psi)/(3177psi)= 3.88

Nbgear =(12300 psi)/(2842psi)= 4.33

Buckingham pioneered this work

equal to 1

same as for bending

d= pitch diameter of smaller gear

Gear Failure

Surface Failure

• from bending of teeth
• infinite life possible
• failure can be sudden
• from contact b/n of teeth
• infinite life not possible
Geometry Factor I

considers radius of curvature of teeth and pressure angle

top sign is for external gears, bottom for internal

For example: p=0.691, g=1.87, I=0.095

Elastic Coefficient

considers differences in materials

For example, Cp=1960 psi

from Table 11-21

same as for bending

Surface-Fatigue Strengths

c is great, but what do I compare it to?

Life Factor CL

to adjust test data fro 1E7 to any number of cycles

Hardness Ratio CH

to account for pitting resistance

when pinion is harder than gear, then gear is cold-worked

only apply CH to the cold-worked gear

when HBp=HBG, then CH=1

gear

pinion

Gear Design

Same for Pinion and Gear

• pd (pc), , F
• Power
• W, Wt, Wr
• Vt
• Nc

Different for Pinion and Gear

• d, N
• T,  ,
• Nb
Gear Design Strategy

Given or Set:

gear ratio

Power, , T

Properties of Gears to Determine:

dp, dg, Np, Ng

pd, F -OR- Safety Factors

(the others are given)

Wt

Bending & Surface Stresses

Safety Factors or pd and F